Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is a process where one function is applied to the result of another function. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

If f(x) = 2x and g(x) = 3x + 1, what is (f ∘ g)(x)?

Back

(f ∘ g)(x) = f(g(x)) = f(3x + 1) = 2(3x + 1) = 6x + 2.

Front

What is the notation for the composition of functions?

Back

The notation for the composition of functions is f ∘ g, which means 'f of g'.

Front

If f(x) = x^2 and g(x) = x + 3, find (g ∘ f)(2).

Back

(g ∘ f)(2) = g(f(2)) = g(2^2) = g(4) = 4 + 3 = 7.

Front

What is the domain of the composition of functions?

Back

The domain of (f ∘ g) is the set of all x in the domain of g such that g(x) is in the domain of f.

Front

If f(x) = 1/x and g(x) = 3x + 2, find f(g(x)).

Back

f(g(x)) = f(3x + 2) = 1/(3x + 2).

Front

What is the range of the function f(x) = 1/x?

Back

The range of f(x) = 1/x is all real numbers except 0.

Front

If f(x) = 2x and g(x) = x^2 - 1, find f(g(3)).

Back

g(3) = 3^2 - 1 = 8, so f(g(3)) = f(8) = 2(8) = 16.

Front

What is the difference between f(g(x)) and g(f(x))?

Back

f(g(x)) applies g first and then f, while g(f(x)) applies f first and then g. They can yield different results.

Front

If f(x) = x + 1 and g(x) = x - 1, what is (f ∘ g)(x)?

Back

(f ∘ g)(x) = f(g(x)) = f(x - 1) = (x - 1) + 1 = x.